Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0536)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=1

http://functions.wolfram.com/07.22.03.0536.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 7/2}, -z] == (1/(228898897920 z^2)) (4 (2 z (324168075 + 29678515020 z + 109149043248 z^2 + 55459097280 z^3 + 6954371328 z^4 + 282002432 z^5 + 3969024 z^6 + 16384 z^7) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (972504225 + 3025568700 z + 86412480336 z^2 + 52211512512 z^3 + 6816768768 z^4 + 280032256 z^5 + 3960832 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]]) + Pi (972504225 + 3457792800 z + 48409099200 z^2 + 387272793600 z^3 + 215151552000 z^4 + 27539398656 z^5 + 1124057088 z^6 + 15859712 z^7 + 65536 z^8) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (972504225 + 3457792800 z + 48409099200 z^2 + 387272793600 z^3 + 215151552000 z^4 + 27539398656 z^5 + 1124057088 z^6 + 15859712 z^7 + 65536 z^8) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]